Abstract
Grouping by proximity is one of several Gestalt principles that characterize the human visual system's propensity to perceptually organize an array of discrete elements. Previous work by Kubovy and colleagues (1995, 1998) showed that a ‘pure distance model’ (PDM) of grouping by proximity predicts the perceptual organization of all dot lattices (DLs). DLs are multi-stable and typically exhibit at least two predominant perceptual organizations. The PDM quantifies the strength of opposing organizations in terms of perceptual stability, a function of relative inter-dot distance. We have since discovered a larger domain of stimuli we call ‘dot-sampled structured grids’ (DSGs) that can be defined by arbitrary differentiable functions along two axes. Like DLs, DSGs are multi-stable. Unlike DLs, DSGs are not defined by purely local geometric properties and can elicit the perception of curvilinear structure.
We argue that DSGs are a useful tool for the study of perceptual organization. If DLs are to be used effectively we must first understand their geometric properties. We present a geometric analysis of DSGs analogous to Kubovy's (1994) two-parameter space of DLs. We also present results from two experiments in which we used the psychophysical procedure developed by Kubovy and colleagues (1995, 1998) in their work with DLs. We present data from experiments in which we manipulated the density, relative proximity, and curvature of possible contours in DSGs. We found significant effects of each in addition to effects of stimulus duration. In a control experiment we manipulated aperture shape and orientation and found no effect. We show that although grouping by proximity constrains the number predominant organizations in DSGs it does not predict our results: the perceptual organization of DSGs violates the PDM. We conclude that current models of perceptual grouping do not suffice to characterize perceptual organization.